Elia Lapenta will defend his thesis on Monday 28 September at 10:00 AM by zoom meeting on
« Three Essays in Hypothesis Testing ».
Supervisor: Professor Pascal Lavergne
- Professor Ingrid VAN KEILEGOM, KU University, Leuven
- Professor Juan-Carlos ESCANCIANO, University Carlos III, Madrid
- Professor Jean-Pierre FLORENS, UT1 Capitole
- Professor Pascal LAVERGNE, UT1 Capitole
This thesis contains three chapters in Hypothesis Testing for semi and non parametric models. The common features of these chapters are two. First, testing is based on the bootstrap. The test statistics proposed are not asymptotically pivotal. Their null asymptotic distributions are difficult to compute, so they cannot be used for the computation of the critical values. The bootstrap, instead, allows obtaining the critical values in a relatively simple way. All bootstrap tests constructed in this work exploit the information under the null hypotheses.
The second common feature across the works in this thesis is the employment of bias corrections for the computation of the statistics. The testing frameworks are non or semi parametric, so the estimators employed are biased. In these contexts, the use of bias corrections allows improving the performance of the tests. Intuitively, the need to control for estimation bias requires shrinking the set of tuning parameters (bandwidths) admissible for inference. The introduction of bias corrections alleviates this problem, enlarging the set of tuning parameters admissible for testing. This makes the tests more robust to the choice of such parameters. It also allows inference using selection rules that are not admissible without bias corrections, avoiding undersmoothing.
The First and the Third chapter develop new tests for models containing nonparametrically generated variables. Such variables are not observed by the researcher but are nonparametrically identified and estimable. In the Second chapter, testing is developed in a framework where all regressors are observed, but inference employs an iterative bias correction method known as L 2 boosting. This method extends the bias correction used in the first chapter, and its employment in testing is novel in the literature.
The contributions of this thesis are threefold. First, new tests are developed for models involving generated variables. The econometric/statistical literature has mainly focused on estimation for these models, but testing appears to be a relatively unexplored area. Second, the works provide new bootstrap procedures for models involving generated regressors. These procedures are new in the literature, as they need to mimic the estimation error coming from estimating the unobserved variables. Third, bias corrections are implemented for inference in models with and without generated regressors. The use of such bias corrections is novel for the testing problems considered.